Evaluate ∫sinh(4x)dx. ∫sinh(4x)dx=___
Answers
The integral of sin h (4x) with respect to x is 1/4 cosh (4x) + C, based on the formula of integration by substitution and the definition of the hyperbolic cosine.
The integral of sin h (4x) with respect to x can be evaluated as follows:∫sin h(4x)dx We use the formula of integration by substitution :u = 4x; du = 4 dx. Substituting into the integral we have:∫sin h(4x)dx = 1/4 ∫sin h(u)du Integrating using the formula for the integral of hyperbolic sine function:∫sin h(u)du = cosh(u) + C where C is the constant of integration. Replacing u by 4x and using the definition of the hyperbolic cosine:\(cosh (u) = (e^u + e^(-u))/2\), the integral becomes:
∫sin h(4x)dx
= 1/4 ∫sin h(u)du
= 1/4 cosh(4x) + C
Therefore, the value of ∫sin h(4x)dx = 1/4 cosh(4x) + C.
Hence, we can conclude that the integral of sin h (4x) with respect to x is 1/4 cosh (4x) + C.
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Related Questions
line segment CD has coordinates C(-1,9) and D(-7,1). If line segment EF is parallel to line segment CD, what is the slope of line segment EF?
Answers
Answer: Slope of segment EF is -4/3
Answer:
The answer is -3/4
Step-by-step explanation:
:)
(L3) Which triangle illustrates an orthocenter?
Answers
An orthocenter is a point in a triangle that is equidistant from all three vertices. One way to construct an orthocenter in a triangle is to take the centroid of the triangle and reflect it over one of the sides. The point where the reflected centroid intersects the other two sides is the orthocenter.
Another way to construct an orthocenter is to take the circumcenter of the triangle and reflect it over one of the sides. The point where the reflected circumcenter intersects the other two sides is the orthocenter.
One triangle that illustrates an orthocenter is the 30-60-90 triangle, which has sides of length 30, 60, and 90. The orthocenter of this triangle is the point where the three medians intersect.
It is worth noting that there are other triangles that also illustrate an orthocenter, but the 30-60-90 triangle is one of the most commonly used examples.
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the probability distribution for the number of goals the lions soccer team makes per game is given below. number of goalsprobability 00.15 10.10 20.10 30.30 40.35 what is the probability that in a given game the lions will score less than 2 goals? a. 0.25 b. 0.35 c. 0.10
Answers
Answer:
0.35 because above all the probs were below 50 meaning that it was hard for them to even score one goal per game
Step-by-step explanation:
Given the 2 similar triangles, what is the length of LK?
Answers
Answer:
7.5
Step-by-step explanation:
the term similar triangles means they have the same angles and the same scale factor so if we look at rs and jl you see they are 12 and 6. thats is a scale factor of .5 so you take 15 and multiply it by .5 or you can divide it by 2.
The amount of clay students used for their last art project is weighed. The line plot displays the amounts of clay. How much more clay did the students who used of a pound use than the students who used of a pound?
Answers
Answer:
C. 2 \(\frac{1}{4}\)
Step-by-step explanation:
First, calculate the amount of clay that both groups used in total. We can find this by multiplying the amount by the number of students.
Used 3/4 of a pound:
3/4(4) = 3 pounds
Used 1/4 of a pound:
1/4(3) = 3/4 pound
Now, subtract:
3 - 3/4 = 2 and 1/4
Answer
i got it right
C. 2
What is the value of x 2,8,9,7.6,x the mean is 6
Answers
The value of X is 3.4
Disclaimer:
We will consider arithmetic mean in this case as which mean is not mentioned.
The total number of terms are 5
thus, arithmetic mean= 6
6= (2+8+9+7.6+x)/5
30 = 26.6+x
x=30-26.6=3.4
Thus the value of X is 3.4
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Main Answer:x= 3.4
Concept and definitions should be there
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.
To calculate it:
• add up all the numbers,
• then divide by how many numbers there are.
Given data
the value of x 2,8,9,7.6,x the mean is 6
Solving part
As we know that
mean =(sum of the terms)/(Number of terms)
By substituting the values, we get
6=(2+8+9+7.6+x)/5
30= x+26.6
x= 30-26.6
x= 3.4
Final Answer: Thusx= 3.4 is the correct answer.
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Solve the initial value problem, u'= -2tu², u(0)=1 with h = 0.2 on the interval [0,0.4]. Use the 4th order Runge Kutta (R – K) method and compare with exact solution.
Answers
A. The 4th order Runge-Kutta method is employed to solve u' = -2tu^2, u(0) = 1 with h = 0.2 on [0, 0.4], and the obtained numerical solution will be compared with the exact solution.
To solve the initial value problem u' = -2tu^2, u(0) = 1 on the interval [0, 0.4] using the 4th order Runge-Kutta (R-K) method with step size h = 0.2, we can follow these steps:
1. Define the function f(t, u) = -2tu^2.
2. Initialize t = 0 and u = 1.
3. Iterate from t = 0 to t = 0.4 with a step size of h = 0.2 using the R-K method.
Calculate k1 = h * f(t, u).Calculate k2 = h * f(t + h/2, u + k1/2).Calculate k3 = h * f(t + h/2, u + k2/2).Calculate k4 = h * f(t + h, u + k3).Update u = u + (k1 + 2k2 + 2k3 + k4)/6.Update t = t + h4. Repeat step 3 until t reaches 0.4.
5. Compare the obtained numerical solution with the exact solution for evaluation.
Exact Solution:
The given differential equation is separable. We can rewrite it as du/u^2 = -2tdt and integrate both sides:
∫(du/u^2) = ∫(-2tdt)
Solving the integrals, we get:
-1/u = -t^2 + C,
where C is a constant of integration.
Applying the initial condition u(0) = 1, we find C = -1.
Therefore, the exact solution is given by:
-1/u = -t^2 - 1
u = -1 / (-t^2 - 1).
Now, we can compare the numerical solution obtained using the R-K method with the exact solution.
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Expand using the distributive property:
7(3a-2b) + 5(3b-4a) =
Answers
Answer:
the answer is a+b
Step-by-step explanation:
7(3a-2b) +5(3b-4a)
21a-14b+15b-20a
a+b
Gabby buys a new purse for $33. The sales tax in her state is 6%. How much is the sales tax?
Answers
Answer:
$1.98
Step-by-step explanation:
$33.00 x 0.06 = $1.98
a pilot flew 1308.3 miles this week The pilot flew the same number of miles each of 3 days this week. How many miles did the pilot fly each day?
Answers
Answer:
Step-by-step explanation:
The pilot flew 436.1 miles each day.
4. In how many ways can 5 men and 7 women be seated in a row so that no two men are next to each other? You must justify your answer.
Answers
Answer:
3628800 ways if the women are always required to stand together.
To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.
First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).
Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.
Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.
Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.
There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.
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PLEASE HELP
tell whether the lines for each pair of equations are parallel perpendicular or neither
y=-5/6x-4
-10x-12y=-18
Answers
The relationship between the lines is (a) parallel
How to determine the relationship between the linesFrom the question, we have the following parameters that can be used in our computation:
y =-5/6x - 4
-10x - 12y = -18
To determine if the two lines are parallel or not we need to compare their slopes.
Make y the subject
y = -5/6x - 4
y = -5/6x + 3/2
A linear equation represented as
y = mx + c
...has its slope to be m
Using the above as a guide, we have the following:
Slope of the first line = -5/6Slope of the second line = -5/6Since the slopes are equal, the two lines are parallel.
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20) Angel asked some of her friends to write down the types and number of pets they own. The bar graph shown here displays the information she received.
Angel predicts that the next friend she asks will not own a rabbit.
Which statement justifies Angel's prediction?
A) None of Angel's friends owns a rabbit.
B) There are more rabbits owned than birds.
C) There are fewer rabbits owned than any pet.
D) There are just as many birds owned as rabbits.
Answers
Regression analysis is useful when you wish to predict the value of a quantitative variable based on a another quantitative variable.
Select one:
True False
Answers
Regression analysis is a statistical technique used to predict the value of a quantitative variable based on another quantitative variable i.e., the given statement is true.
Regression analysis is widely used when there is an interest in understanding how one quantitative variable, known as the dependent variable or response variable, is influenced by another quantitative variable, known as the independent variable or predictor variable.
The goal is to establish a mathematical relationship between the variables that can be used for prediction and inference.
In regression analysis, a model is built based on the observed data to estimate the relationship between the variables. The model takes into account the variability in the data and provides insights into the strength and direction of the relationship.
By analyzing the model's coefficients, such as the slope and intercept, predictions can be made about the dependent variable's values for different levels of the independent variable.
Regression analysis allows for the assessment of the significance of the relationship, the quantification of the effect of the predictor variable on the response variable, and the estimation of the prediction accuracy.
It provides a valuable tool for making informed decisions, conducting research, and understanding the underlying factors that contribute to the variability of the dependent variable.
Therefore, it is true that regression analysis is useful when predicting the value of a quantitative variable based on another quantitative variable.
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A random sample of 225, 1st year statistics tutorials were selected from the past 5 years and the number of students absent from each one recorded. The results were x = 11.6 and s = 4.1 absences. Estimate the confidence interval of absences per tutorial over the past 5 years with 90% confidence.
Answers
The 90% confidence interval of absences per tutorial over the past 5 years is approximately 11.151 to 12.049 absences.
To estimate the 90% confidence interval of absences per tutorial over the past 5 years, follow these steps:
1. Identify the given data:
Sample size (n) = 225
Sample mean (x) = 11.6
Sample standard deviation (s) = 4.1
Confidence level = 90%
2. Calculate the standard error (SE):
SE = s / sqrt(n)
SE = 4.1 / sqrt(225)
SE ≈ 0.273
3. Determine the critical value (z) for a 90% confidence interval:
For a 90% confidence interval, the critical value (z) is approximately 1.645.
4. Calculate the margin of error (ME):
ME = z * SE
ME = 1.645 * 0.273
ME ≈ 0.449
5. Estimate the confidence interval:
Lower limit = x - ME
Lower limit = 11.6 - 0.449
Lower limit ≈ 11.151
Upper limit = x + ME
Upper limit = 11.6 + 0.449
Upper limit ≈ 12.049
The 90% confidence interval of absences per tutorial over the past 5 years is approximately 11.151 to 12.049 absences.
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PLZ HELP ME!!!!
find x in the given figure.
Answers
The common sparrow has a wingspan of 9 to 15 centimeters. Which inequality matches the wingspan of the common sparrow?
Answers
An inequality that matches the wingspan of the common sparrow is 9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.
In this question, we have been given a statement 'The common sparrow has a wingspan of 9 to 15 centimeters. '
We need to write an inequality that matches the wingspan of the common sparrow.
Let x represents the wingspan of the common sparrow.
According to given statement, the common sparrow has a wingspan of 9 to 15 centimeters.
So, the required inequality would be,
9 ≤ x ≤ 15
Therefore, an inequality that matches the wingspan of the common sparrow is 9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.
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Rectangle R has varying length l and width w but a constant area of 4ft² .
a. Express the perimeter P as a function of l. What kind of function is P? What is its domain?
Answers
The perimeter P of rectangle R with a constant area of 4ft² can be expressed as a function of the length l as 2l+8/l. The function is linear, and its domain includes all positive values of l.
Let's consider a rectangle with length l and width w, such that its area is constant at 4ft². The area of a rectangle is given by A = l * w.
In this case, we have A = l * w = 4ft².
To find the perimeter P, we use the formula P = 2l + 2w.
Since we want to express P as a function of the length l, we need to eliminate the variable w. From the area equation, we can solve for w:
w = 4ft² / l.
Substituting this value of w into the perimeter formula, we have:
P = 2l + 2(4ft² / l).
Simplifying further, we get:
P = 2l + 8ft² / l.
This expression represents the perimeter P as a function of the length l. It is a rational function, as it involves the division of polynomials. The domain of this function includes all positive values of l, as length cannot be negative or zero in this context.
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You fill a cone with strawberry ice cream with a radius of 8.1 cm and height of 90 cm what is the height and radius of the strawberry ice cream
Answers
Solve the inequality.−8≤2/5(k−2)
The / is not a division sign.
Answers
Answer: x is grater or equal to -18
Inter el notation
[-18,oo)
Step-by-step explanation:
plz help right now illl give brainlist 5.0 and say thanks
Answers
Answer: 4+4+1
Step-by-step explanation: 4+4+1=4+5
Hope this helps!
At a price of $162.65 per ounce the daily demand of virbog is 850 ounces. At a price of $132.05 the daily demand of virbog is 1450 ounces. Use this information to create two ordered pairs of the form (Quantity Demanded, Price per Ounce). Use a comma to separate the ordered pairs. At a price of $162.65 per ounce the daily demand of virbog is 850 ounces. At a price of $132.05 the daily demand of virbog is 1450 ounces. Use this information to create two ordered pairs of the form (Quantity Demanded, Price per Ounce). Use a comma to separate the ordered pairs.
Answers
The first ordered pair is (850, 162.65), indicating that at a price of $162.65 per ounce, the daily demand of Virbog is 850 ounces. The second ordered pair is (1450, 132.05), indicating that at a price of $132.05 per ounce, the daily demand of Virbog is 1450 ounces.
These ordered pairs represent the relationship between the quantity demanded and the price per ounce of Virbog. It shows how the demand for Virbog changes with respect to its price.
The first ordered pair indicates that as the price per ounce increases to $162.65, the quantity demanded decreases to 850 ounces. The second ordered pair indicates that as the price per ounce decreases to $132.05, the quantity demanded increases to 1450 ounces. This information can be used to analyze the demand curve for Virbog and study its price elasticity.
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What is the equation of the line in point slope form with a slope of m=-2/3 passing through the point (-5,-2)
Answers
Answer:
\(m=− 32 ≈−0.666666667\)
Step-by-step explanation:
Find the value of p and q form the following equal ordered pairs: (8q-2,2-7q)=(6,q+6)
Answers
Compare both pairs
\(\\ \rm{:}\dashrightarrow 8q-2=6\)
\(\\ \rm{:}\dashrightarrow 8q=6+2\)
\(\\ \rm{:}\dashrightarrow 8q=8\)
\(\\ \rm{:}\dashrightarrow q=\dfrac{8}{8}\)
\(\\ \rm{:}\dashrightarrow q=1\)
And
\(\\ \rm{:}\dashrightarrow 2-7p=p+6\)
\(\\ \rm{:}\dashrightarrow 2-6=8p\)
\(\\ \rm{:}\dashrightarrow p=-1/2\)
A store sells 5 T-shirts for $48.60. What is the unit cost per T-shirt? A. $9.72 B. $8.10 C. $43.60 D. $0.10
Answers
Answer:$9.72
Step-by-step explanation: 48.60 DIVIDED BY 5 EQUALS 9.72
GIVE ME BRAINLEST PLSS
Three vertices of quadrilateral ABCD are A(-4,3), B(-1,5), and D(4,-1), as shown below.
In order for ABCD to be a parallelogram, what must be the coordinates of point C?
A. (-1, -7)
B. (1.5, 2)
C. (2, -4)
D. (7, 1)
Answers
Answer:
my answer is letter c thats may answer
) Himari is solving the equation 4 (x - 3) = 16. Her first step is 4x - 12 = 16.
Which step could be the next step? Select all that apply.
1) 4x -12 + 12 = 16 + 12
2) 4x - 12-(-12) = 16 - (-12)
3) 1/4 • (4x - 12) = 16 • (1/4)
4) 4x/4 - 12 = 16/4
5) 4 • (4x - 12) = 16 • 4
Answers
Answer: it would be 1 and 2
Step-by-step explanation:
It would be number two because to negatives make a positive like this.
16-(-12) is the same as 16+12 and 12-(-12) is the same as 12+12
4(x-3)=16
4x-12=16
4x=16+12
4x=28
x=7
Linda was selling tickets to the school play. She sold 10 more adult tickets than children’s tickets and sold twice as many senior tickets as children’s tickets. If she sold 218 tickets, how many were adult tickets
Answers
Answer:
Totals can change but the pattern remains the same: Linda sold 40 Senior's Tickets, 30 Adult's Tickets, and 20 Children’s Tickets, for a total of 90 tickets sold.
Step-by-step explanation:
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The function p is defined as p(x) = x2 – 3x. If the
function q is defined as q(x) = p(x) – 4, what is the
value of q(10) ?
A) -30
B) 6
C)
66
D) 70
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
\(q(x) = {x}^{2} - 3x - 4\)
\(q(10) = ( {10})^{2} - (3 \times 10) - 4 \)
\(q(10) = 100 - 30 - 4\)
\(q(10) = 70 - 4\)
\(q(10) = 66\)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Thus the correct answer is (( C )) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
(1 point) a rectangular swimming pool is 8 ft deep, 20 ft wide and 20 ft long. if the pool is filled to 1 ft below the top, how much work is required to pump all the water into a drain at the top edge of the pool? (use 62.4 lb/ft2 for the weight density of water.)
Answers
This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.
What is amount?Amount is a numerical value that refers to the total sum of money or other type of payment due. It is used to quantify the size of a transaction, the cost of goods or services, or any other type of financial transaction. Amounts can be expressed in a variety of different currencies, and they can be negative (owing) or positive (owed).
To calculate the amount of work required to pump all the water from the rectangular swimming pool into a drain at the top edge, we must first calculate the volume of the water in the pool. Volume is calculated by multiplying the length, width, and depth of the pool, which in this case is 20 ft x 20 ft x 8 ft = 3,200 cubic ft. Since the pool is filled to 1 ft below the top, the volume of water is 3,200 ft3 - 20 ft3 = 3,180 ft3.
Next, we must calculate the weight of the water, which is the volume multiplied by the weight density of water (62.4 lb/ft3). The weight of the water in the pool is 3,180 ft3 x 62.4 lb/ft3 = 197,952 lbs.
Finally, to calculate the amount of work required to pump the water from the pool into a drain at the top edge, we must multiply the weight of the water (197,952 lbs) by the height of the drain (8 ft). This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.
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